The present invention relates generally to three-dimensional (3D) computerized tomography (CT) and, more particularly, to methods and apparatus employing parallel processing for reconstructing a 3D image of an object from cone beam projection data.
In conventional computerized tomography for both medical and industrial applications, an x-ray fan beam and a linear array detector are employed. Two-dimensional (2D) imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time. When a 3D image is required, a "stack of slices" approach is employed. Acquiring a 3D data set a 2D slice at a time is inherently tedious and time-consuming. Moreover, in medical applications, motion artifacts occur because adjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal, because the distance between slices is typically less than the x-ray collimator aperture, resulting in double exposure to many parts of the body.
A more recent approach, based on what is called cone beam geometry, employs a two-dimensional array detector instead of a linear array detector, and a cone beam x-ray source instead of a fan beam x-ray source, for much faster data acquisition. To acquire cone beam projection data, an object is scanned, preferably over a 360.degree. angular range, either by moving the x-ray source in a circular scanning trajectory, for example, around the object, while keeping the 2D array detector fixed with reference to the source, or by rotating the object while the source and detector remain stationary. In either case, it is relative movement between the source and object which effects scanning, compared to the conventional 2D "stack of slices" approach to achieve 3D imaging of both medical and industrial objects, with improved dose utilization.
However, image reconstruction becomes complicated and requires massive computational power when a 3D image is reconstructed from cone beam projection data, in contrast to reconstruction of a 2D image from fan beam projection data.
Literature discussing the cone beam geometry for 3D imaging and generally relevant to the subject matter of the invention includes the following: Gerald N. Minerbo, "Convolutional Reconstruction from Cone-Beam Projection Data", IEEE Trans. Nucl. Sci., Vol. NS-26, No. 2, pp. 2682-2684 (Apr. 1979); Heang K. Tuy, "An Inversion Formula for Cone-Beam Reconstruction", SIAM J. Math., Vol. 43, No. 3, pp. 546-552 (June 1983); L. A. Feldkamp, L. C. Davis, and J. W. Kress, "Practical Cone-Beam Algorithm", J. Opt. Soc. Am.A., Vol. 1, No. 6, pp. 612-619 (June 1984); Bruce D. Smith, "Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods", IEEE Trans. Med. Imag., Vol. MI-44, pp. 14-25 (March 1985); and Hui Hu, Robert A. Kruger and Grant T. Gullberg, "Quantitative Cone-Beam Construction", SPIE Medical Imaging III: Image Processing, Vol. 1092, pp. 492-501 (1989). In general, this literature discloses various formulas for reconstruction of an image, including the use of a 3D Fourier transform or a 3D Radon transform. Questions of data completeness achieved with various source scanning trajectories are also considered.
The present invention is an implementation of the Algebra Reconstruction Technique (ART) for reconstructing an image of an object from its projections. The ART is an iterative algorithm which uses raysums to correct each voxel (volume element) of the reconstructed image at each iteration. The ART was initially disclosed in Richard Gordon, Robert Bender and Gabor T. Herman, "Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography", J. Theor. Biol., 29, pp. 471-481 (1970). Details regarding the mathematical foundations of the ART algorithm were described in Gabor T. Herman, Arnold Lent and Stuart W. Rowland, "ART: Mathematics and Applications--A Report on the Mathematical Foundations and on the Applicability to Real Data of the Algebraic Reconstruction Techniques", J. Theor. Biol., 43, pp. 1-32 (1973). Extension of the additive ART to 3D cone beam geometry is described in M. Schlindwein, "Iterative Three-Dimensional Reconstruction from Twin-Cone Beam Projections", IEEE Trans. Nucl. Sci., Vol. NS-25, No. 5, pp. 1135-1143 (October 1978). The ART was recently used for vascular reconstruction, as reported in A. Rougea, K. M. Hanson and D. Saint-Felix, "Comparison of 3-D Tomographic Algorithms for Vascular Reconstruction", SPIE, Vol. 914 Medical Imaging II, pp. 397-405 (1988).
In general, the Algebra Reconstruction Technique requires a large amount of computation time, and has not been implemented with parallel processing techniques.
In view of the parallel processing aspect of the present invention, the system described in Richard A. Robb, Arnold H. Lent, Barry K. Gilbert, and Aloysius Chu, "The Dynamic Spatial Reconstructor", J. Med. Syst., Vol. 4, No. 2, pp. 253-288 (1980) is relevant. The Dynamic Spatial Reconstructor employs twenty-eight x-ray sources and twenty-eight x-ray imaging systems in a synchronous scanning system to acquire data all at one time for a subsequent "stack of slices" reconstruction using conventional 2D reconstruction algorithms. The Robb et al. reference refers to the use of "high-speed parallel processing techniques" for the reconstruction computation.